| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |linear| > constant (greater than) |
| Difficulty | Moderate -0.8 This is a straightforward modulus question requiring standard techniques: sketching a V-shaped graph by identifying the vertex at x=4, solving an equation by considering two cases (8-2x=±4), and solving an inequality using the same approach. All parts are routine textbook exercises with no problem-solving insight required, making it easier than average but not trivial since it requires correct application of modulus properties. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Modulus graph V shape in 1st quadrant going into 2nd quadrant, touching \(x\)-axis, must cross \(y\)-axis | M1 | Condone not ruled |
| 4 and 8 labelled | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = 2\) | B1 | One correct answer |
| \(x = 6\) | B1 | Second correct answer and no extras; condone answers shown on graph if clearly indicated |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x > 6\) | B1 | One correct answer |
| \(x < 2\) | B1 | Second correct answer and no extras and no further incorrect statement e.g. \(6 < x < 2\) or \(2 < x > 6\). SC \(x \geq 6\), \(x \leq 2\) scores B1 |
## Question 4(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Modulus graph V shape in 1st quadrant going into 2nd quadrant, touching $x$-axis, must cross $y$-axis | M1 | Condone not ruled |
| 4 and 8 labelled | A1 | |
## Question 4(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = 2$ | B1 | One correct answer |
| $x = 6$ | B1 | Second correct answer and no extras; condone answers shown on graph if clearly indicated |
## Question 4(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x > 6$ | B1 | One correct answer |
| $x < 2$ | B1 | Second correct answer and no extras and no further incorrect statement e.g. $6 < x < 2$ or $2 < x > 6$. SC $x \geq 6$, $x \leq 2$ scores B1 |
---4
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = | 8 - 2 x |$.
\item Solve the equation $| 8 - 2 x | = 4$.
\item Solve the inequality $| 8 - 2 x | > 4$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2010 Q4 [6]}}